饱和非线性切换系统的L_2-增益分析与设计

L_2-gain Analysis and Design for Nonlinear Switched Systems Subject to Actuator Saturation

基于线性矩阵不等式和干扰抑制理论,利用多李雅普诺夫函数方法研究了一类具有执行器饱和的非线性切换系统的L2-增益分析及控制综合问题。首先,当假设控制器事先给定时,给出了保证闭环系统在外部扰动作用下状态轨迹有界的充分条件。然后根据这一条件,将估计容许干扰能力的问题转化为一个受限优化问题。然后,在容许干扰集合内,对系统的受限L2-增益进行分析。通过解一个受限优化问题估计了受限L2-增益的上界。进一步,当控制器增益矩阵为设计变量时,这些优化问题可方便地应用于控制器设计问题之中。所有结果都可通过解带有线性矩阵不等式约束的凸优化问题获得。

By utilizing the multiple Lyapunov function method, the analysis and control of L2-gain is studied for a class of uncertain switched linear systems with saturating actuators based on LMIs. Firstly, when controllers are pre-given, a sufficient condition is established, which guarantees that the trajectories of the system with the L2 disturbances are bounded. According to this condition, the problem of estimating disturbance tolerance capability is formulated as a constrained optimization problem. Then, the restricted L2-gain property is analyzed over the set of tolerable disturbances. An upper bound on the restricted L2-gain is estimated by solving a constrained optimization problem. Furthermore, when controller gain matrices are design variables, these optimization problems can be applied to the controller design. All results are presented by a LMIs optimization-based approach.